Figure REF  shows results from a simulation with \(n_i=84n_c\)  and \(\alpha =2.3\%\) . Large-amplitude short-wavelength plasma oscillations are excited by the positron beam [Fig. REF (a)]. The positrons pile up while being pushed inwards by the laser, explaining the appearance of high positron density (\(n_p\sim 23n_c\) ). The density of the trailing electrons is \(n_e\sim 110n_c\)  \((\simeq n_i+n_p)\) , indicating the perturbation of electron density is roughly the same as the positron driver. In contrast, the maximum density perturbation in the pure electron-ion target is only \(\sim 7n_c\)  close to the surface. The electrons undergo a density modulation with a wavelength of \(\sim 0.007c/\omega _0\)  which corresponds to the plasma wavelength, i.e., \(\lambda _p\simeq 2\pi v_p/\omega _{pe}\) , where \(\omega _{pe}=8.8\omega _{0}\)  and the bulk positron velocity at this moment is \(\sim 0.01c\) , indicating the onset of beam-plasma instability [1]}. The positrons are accelerated to a peak bulk velocity of \(0.03c\)  by \(t=50\omega _{0}^{-1}\) , in agreement with Eq. (REF ). The positron beam starts to stretch in velocity space when travelling across the excited plasma waves. Eventually, some positrons are further accelerated with velocities reaching \(0.3c\) , while \(\sim 50\%\)  of the positrons carry negative momenta forming a positron reflux [Fig. REF (b)]. The positron reflux shows a high velocity tail reaching \( \sim -0.2c\) , and a significant number of electrons also carry negative momenta with a tail velocity \(\sim -0.14c\) , resembling the positron driver. In the pure electron-ion target, however, the reflux of electrons is negligible.
